Velocity dependent interactions and a new sum rule in bcc He

Recent neutron scattering experiments [PRL,{\bf 88},p.195301 (2002)] on solid $^4$He, discovered a new optic-like mode in the bcc phase. This excitation was predicted by a recently proposed model that describes the correlated atomic zero-point motion in bcc Helium in terms of dynamic electric dipole moments. Modulations of the relative phase of these dipoles between different atoms describes the anomalously soft T$_1$(110) phonon and two new optic-like modes, one of which was recently found in the neutron scattering experiments. In this work we show that the correlated dipolar interactions can be written as a velocity dependent interaction. This then results in a modified f-sum rule for the T$_1$(110) phonon, in good agreement with the recent experimental data.Comment: 5 pages, 3 figure

Modeling the dynamics of a tracer particle in an elastic active gel

The internal dynamics of active gels, both in artificial (in-vitro) model systems and inside the cytoskeleton of living cells, has been extensively studied by experiments of recent years. These dynamics are probed using tracer particles embedded in the network of biopolymers together with molecular motors, and distinct non-thermal behavior is observed. We present a theoretical model of the dynamics of a trapped active particle, which allows us to quantify the deviations from equilibrium behavior, using both analytic and numerical calculations. We map the different regimes of dynamics in this system, and highlight the different manifestations of activity: breakdown of the virial theorem and equipartition, different elasticity-dependent "effective temperatures" and distinct non-Gaussian distributions. Our results shed light on puzzling observations in active gel experiments, and provide physical interpretation of existing observations, as well as predictions for future studies.Comment: 11 pages, 6 figure

Activity driven fluctuations in living cells

We propose a model for the dynamics of a probe embedded in a living cell, where both thermal fluctuations and nonequilibrium activity coexist. The model is based on a confining harmonic potential describing the elastic cytoskeletal matrix, which undergoes random active hops as a result of the nonequilibrium rearrangements within the cell. We describe the probe's statistics and we bring forth quantities affected by the nonequilibrium activity. We find an excellent agreement between the predictions of our model and experimental results for tracers inside living cells. Finally, we exploit our model to arrive at quantitative predictions for the parameters characterizing nonequilibrium activity, such as the typical time scale of the activity and the amplitude of the active fluctuations.Comment: 6 pages, 4 figure

Spatial fluctuations at vertices of epithelial layers: quantification of regulation by Rho pathway

In living matter, shape fluctuations induced by acto-myosin are usually studied in vitro via reconstituted gels, whose properties are controlled by changing the concentrations of actin, myosin and cross-linkers. Such an approach deliberately avoids to consider the complexity of biochemical signaling inherent to living systems. Acto-myosin activity inside living cells is mainly regulated by the Rho signaling pathway which is composed of multiple layers of coupled activators and inhibitors. We investigate how such a pathway controls the dynamics of confluent epithelial tissues by tracking the displacements of the junction points between cells. Using a phenomenological model to analyze the vertex fluctuations, we rationalize the effects of different Rho signaling targets on the emergent tissue activity by quantifying the effective diffusion coefficient, the persistence time and persistence length of the fluctuations. Our results reveal an unanticipated correlation between layers of activation/inhibition and spatial fluctuations within tissues. Overall, this work connects the regulation via biochemical signaling with mesoscopic spatial fluctuations, with potential application to the study of structural rearrangements in epithelial tissues.Comment: 8 pages, 3 figure

Bcc 4^4He as a Coherent Quantum Solid

In this work we investigate implications of the quantum nature of bcc $^{4}$% He. We show that it is a unique solid phase with both a lattice structure and an Off-Diagonal Long Range Order of coherently oscillating local electric dipole moments. These dipoles arise from the local motion of the atoms in the crystal potential well, and oscillate in synchrony to reduce the dipolar interaction energy. The dipolar ground-state is therefore found to be a coherent state with a well defined global phase and a three-component complex order parameter. The condensation energy of the dipoles in the bcc phase stabilizes it over the hcp phase at finite temperatures. We further show that there can be fermionic excitations of this ground-state and predict that they form an optical-like branch in the (110) direction. A comparison with 'super-solid' models is also discussed.Comment: 12 pages, 8 figure